tmci {ctmcd}

Delta Method Confidence Intervals for Matrix Exponential Transformations of Generator Matrix Objects

Description

Generic function to derive delta method based confidence intervals for matrix exponential transformations of "EM" based generator matrix objects

Usage

tmci(gmem, alpha, te, eps = 1e-04, expmethod = "PadeRBS")

Arguments

gmem

an "EM" generator matrix object

alpha

significance level

te

discrete time horizon for which the interval is supposed to be computed

eps

threshold for which generator matrix parameters are assumed to be fixed at zero

expmethod

method to compute matrix exponentials (see ?expm from expm package for more information)

Details

Confidence intervals for discrete-time transition matrix predictions given generator matrix estimates are computed by using the delta method for matrix exponential transformations.

Value

transition matrix confidence bounds

References

G. dos Reis, M. Pfeuffer, G. Smith: Capturing Rating Momentum in the Estimation of Probabilities of Default, With Application to Credit Rating Migrations (In Preparation), 2018

Examples

data(tm_abs)

## Maximum Likelihood Generator Matrix Estimate
gm0=matrix(1,8,8)
diag(gm0)=0
diag(gm0)=-rowSums(gm0)
gm0[8,]=0

gmem=gm(tm_abs,te=1,method="EM",gmguess=gm0)

## 2.5 Year Transition Matrix Confidence Interval
citm=tmci(gmem,alpha=0.05,te=2.5)
citm